Problem Statement

There are $N$ people standing on a number line. The people are numbered $1, 2, \ldots, N$, and initially person $i$ is at coordinate $S_i$. Here, the $S_i$ are pairwise distinct.

You can repeatedly perform the following operation.

• Choose one person. Let $x$ be the coordinate where that person currently is, and move them to $x - 1$ or $x + 1$. If there is a person at the destination, that person is simultaneously moved to coordinate $x$.

Find the minimum number of operations required to reach a state where each person $i$ is at coordinate $T_i$. Here, the $T_i$ are pairwise distinct.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq S_i, T_i \leq 10^9$
• $S_i \neq S_j$ and $T_i \neq T_j$ if $i \neq j$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

• $N$
• $S_1$ $S_2$ $\ldots$ $S_N$
• $T_1$ $T_2$ $\ldots$ $T_N$

Output

Output the answer.

3
4 2 5
3 4 1

6

Initially, persons $1, 2, 3$ are at coordinates $4, 2, 5$, respectively. By performing the operations as follows, persons $1, 2, 3$ end up at coordinates $3, 4, 1$, respectively, in six operations.

• Move person $1$ from coordinate $4$ to $3$. After this operation, persons $1, 2, 3$ are at coordinates $3, 2, 5$, respectively.
• Move person $1$ from coordinate $3$ to $2$. Since person $2$ is at coordinate $2$, person $2$ simultaneously moves to coordinate $3$. After this operation, persons $1, 2, 3$ are at coordinates $2, 3, 5$, respectively.
• Move person $3$ from coordinate $5$ to $4$. After this operation, persons $1, 2, 3$ are at coordinates $2, 3, 4$, respectively.
• Move person $3$ from coordinate $4$ to $3$. Since person $2$ is at coordinate $3$, person $2$ simultaneously moves to coordinate $4$. After this operation, persons $1, 2, 3$ are at coordinates $2, 4, 3$, respectively.
• Move person $3$ from coordinate $3$ to $2$. Since person $1$ is at coordinate $2$, person $1$ simultaneously moves to coordinate $3$. After this operation, persons $1, 2, 3$ are at coordinates $3, 4, 2$, respectively.
• Move person $3$ from coordinate $2$ to $1$. After this operation, persons $1, 2, 3$ are at coordinates $3, 4, 1$, respectively.

4
2 4 5 9
2 4 5 1

11

6
5 2 9 1 6 8
1 4 7 0 9 3

13

• Source: AtCoder ABC 479 F